Introduction to combinations | Probability and Statistics | Khan Academy
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Imagine going to sleep every night , resting and knowing you have helped so many people out there to learn! Hats off to you man
Yeah, and as a viewer image going to bed knowing you just learnt so much and actually understood it. (Something schools are not very good at)
He really has changed the world. I watched these in highschool during the late 2000s and again, in 2020, I've come back to refresh some concepts! The legacy of Khan Academy is incredible
Sumblero
dude thank you so much, we don't have online classes and our school just sent us worksheets to do.Thanks a bunch man
This was very helpful! I'm 34 and last year I decided to go back to university. this semester I'm taking statistics intro and I have never seen or heared of permutations and combinations. This video explained it all in less than 10 min. Thanks Khan (or whoever is talking in the video).
His name is Sal Khan fyi
@@keevankk873 Salman khan
How did uni go? Good luck!
@@h.k3260 Graduated last semester 👍🏼
Congrats! @@salimalajmi4691
thanks for not making me feel stupid anymore
In case someone is wondering "what possibly could those 20 combinations be?" well here they are
ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF, BCD, BCE, BCF, BDE, BDF, BEF, CDE, CDF, CEF, DEF
Thanks man
good man
He's used all three by now "have sitted", "have sat" and "have sitten".
+Alexander Steshenko My mind is so tired trying to grasp combinations but your comment just made me laugh out loud!😂😂
Thank you so much!
Cera its hard
neological thought is the expression of genius.
Alexander Steshenko 😂
Those who have difficulty imagining this concept logically, Let me put in simple words !
First you calculate permutation for given question, as you know permutation generates all the ways we can arrange elements, including duplicates!
Now to calculate combinations, all we have to remove duplicates.
For question A,B,C,D,E,F and total spots available is 3, then permutation would be 120
And if we want to calculate combinations, all we have to remove the duplicates from our permuations.
So if we calculate, how many ways we can arrange 3 people at 3 spots, the answer would be 6. Meaning, that each 3 letters produces 6 different mutations, for which we should count 1 in case of calculating combinations. So if we divide total permutations by toatl dupllicates generated by each 3 letters at a time. The answer would be 20.
Conclusion : Permutation tells us all the ways including duplicates as well (according to combinations point of view)
So to calcuate combination all we have to remove is the duplicates generated by n spots permuation.
Now, I understand the formula for combinations. Thank you!
You explain the origin of the concepts so well which is something often neglected! Thank you!!
So, is a combination lock misnamed? Is the true name of a combination lock a permutation lock?
yes
UltimateBargains omg lol my teacher told us that in like the sixth grade. I finally know what she meant!
super explanation. no formulas needed. back to basics. another hat off for you professor.
Well explained! Thanks! All this while I didn't know the concept of combinations
Very helpful. I've been racking my brain going through a lot of different lectures trying to understand the difference between the two but this video cleared it up. Thank you
Really well explained, it all came together at the end, THANK YOU!
very good explanation, thanks a lot!
Thanks a lot sir you clear out my confusion
made it simple thanks
Thank you!
Thank you for this video!
omg tysm im in 7th and i have a quiz tmr first period and I have no idea what to do and this helped a lot so ty omg
Such a beautiful explanation
Thankyou for providing such vedioa
This dude is simply awesome
Thank you for this detailed tutorial on combinations, sir!
He's a Godly being🔮
This video explained probability and statistics so much thank you or this video
He is a great teacher
Wow, I now know how to calculate possible combinations of stuff
I literally had no idea until now, what does combination even mean, despite I've completed 2 yrs of my statistics education 😁😁😂😂😂😂😂
Kudos sir....
This dude is great at teaching
Tnx a lot man
I know this video is old but im doing somthing that may involve revisting this concept and i realize that I may not be 100 percent sure i understand it. Is another way to think of combinations as from all the possible ways to rearrange in this video the example is 3 from 5 how many sets can i make ( were each set will have different letters) but first one must find out the how many groups of 3 count as 1 set. ( which is the same as how many different groups of 3 one can make from 3 things) then by dividing the number of permutation by this number one can determine how many sets they can make?
Thank you so mach Sal wish u all the best❤
This is better than your old combinations video. Thank you! :)
You are a true genius, I like the way you write, the way you speak and illustrate things in a simple way, thanks a lot !!
I really struggled with math since I was a kid and none of the teachers took the time to explain how simple topics such as ratio and trigonometry works. It wasn't until I was took math again in college I met this 1 lecturer who took the time to explain things in a different way, 8 finally understood and scored an A* for which I'm so proud of even today.
It just takes that one teacher and your entire understanding opens up and that was why I went on to get a Ba Hons degree in primary education. He was such an inspiration and strangely looked exactly like kiefer sutherland. (And yes I did make him say "previously on 24 lo.).
Just awesome 🤯
Thank you sir
Great explanation 💛💛💛😍
Thank you so much sir!!🙏🙏🙏🙏🙏🙏🙏
Hi sir. I am Renalyn Tavarra a BSED Math Student and I would like to ask for your permission to allow me to use this video tutorial of yours about combination and attach the link of it on my unit plan. I hope you consider this. Thank you and God bless.
I shoud send this to my math teacher so he could learn from this
Thank you so much sal sir.
So, the reason why we divide the number of arrangements/permutations by the number of arrangements in a combination group is that because now that we don't care about the order, we consider the (in this case) 6 arrangements in a combination group of (in this case) 3 letters as one whole entity/one group that contain 3 letters in it because that's all that matters now that we don't care about the order.
I'm kinda slow why is the number of ways 6, is it because there are 6 people
You're going to the Good Place
How to go about deriving the formula number of ways of choosing r objects from p objects of one type, q objects second type and so on
Waw noice tutoreal
Permutations include all possible arrangements.
Combinations are only about inclusion and not arrangements.
thanks
This video Help me lot to understand the concept about combination thnx 🤩
You are our GURU
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your videos should be sent in the next Voyager
I am using my moms computer to do better in caribou contest. thanks dude
You shouldve known that people who came here is for the
2* in terms of c(n,r)
How would you go about setting up a problem for seating these people (A - F) for more than 6 seats? Or is this addressed in a separate video?
patrickstar2014 hahaha I don't think you could because no one would be sitting in the "greater than six"th seat.
patrickstar2014 nice thought though.
But what if you were considering A B C D _ E F to be a different seating arrangement than A B C _ D E F
For example I have 13 seats and 7 people. The permutation would be 13! : 6! = 8648640 ways of seating 7 people on 13 chairs. Because 13 x 12 x 11 x 10 x 9 x 8 x 7 and the rest of the chairs are empty. The combination would be (13! : 6!) : 7!, which is the same as 13! : (6! x 7!). Because in a combination the order of the people does no matter. So you divide 8648640 by the amount of ways you can arrange 7 people, which is 7! or 5040. The answer to 13! : (6! x 7!) = 1716
patrickstar2014 If you had one gap, you would class the gap as another person.
Thanks
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How could we possibly know the number of ways to arrange 3 people (i.e 6) without having to write out all the possible ways? Seems very inefficient to think out ABC, BAC, CAB, etc... especially if this number was much larger than just 3?
Thanks!!
go to the permutation videos...u will see there...ik it's late thoughh😂😅
Great
For the sake of my intuition and lack of understanding I guess, I can't help but think that if 1 set of 3 people can have 6 different permutations then, why not divide by (3! - 1) ? since we require any 1 of the 6 permutations only. Can someone pls explain that to me? I think it has to with the division more than the numerical analysis.
Wicked
Leave to a college course to complicate counting. lol
Oh dear, it appears a system error caused the transaction to stray to an invalid email!
i love u sal
System malfunction: transaction misplaced in the realm of invalid emails!
How many combinations of 6 digits are there if the pool of digits are 1-69 and a second pool 1-26. Conditions only allow digits 1-26 can be chosen twice, but only once per pool for each combination?
yes
Why is this soooo hard
IDK LOL
who else watched this inside school
Answer should be 10 right. Because when we split 6 people into group of 3 then 6C3 = 20 but in that 20 , 10 will be the duplicates of other 10. So it should be 10. If it we are not splitting them into group of 3 then 6CK ( K = 3 ) is correct .
No In order to help you understand better I have literally listed all possible 20 combinations for ABCDEF in sets of 3 and no they are not duplicates
ABC
ABD
ABE
ABF
ACD
ACE
ACF
ADE
ADF
AEF
BCD
BCE
BCF
BDE
BDF
BEF
CDE
CDF
CEF
DEF
so what is the number of permutations if the number of chairs is 60 but the number of people is 5? Wouldn't the answer be negative according to the formula?
Ultimate Ldrago That's dumb as rationally your not gonna get 60 chairs for 5 people
nope,
the answer will be
655381440 permutaions
&
5461512 combinations
You just have to assume the large amount as "the persons" and the less amount as "chairs"...
Suppose,
If there was "6 chairs and 3 persons" instead of "3 chairs and 6 persons" the result would be the same...
You have to understand, the chair and the persons are just for "understanding purpose" only...
The combinations is what matters and it will be in the same way...
800th like!
802 here
I’m in grade 7 and I have to learn this by myself and present it
Ah i guess by your profile
me spend 30' sitting trying to understand it but didnt help
6' of this video:
why dont i get it... what why is permutation related to combination at all...
Permutation is when you are just shifting the positions of all elements of a set and counting how many “shifting possibilities there can be”.
Combination is more like if you are selecting a smaller number of elements from a larger set and counting how many selection you can make or shifting the selected elements and counting how many shifts there can be.
... Okay so is this formula useful for figuring out how many possible combinations a bike lock might have?
It would probably be permutation because the order matters but yep
Shouldn't it be divided by 3!?
How come when u flip a coin 3 times the choose value for 2 heads is 3 ? HHT, HTH , THH ? Isn’t that a permutation instead of a combination yet the binomial coefficient uses a combination?
yes
why is the first question a permutation not a combination since order of the seating doesnt matter?
shaw shaw it did matter for the top part or the first park.
To understand clearly... :)
Our teacher: we name the people Person A, Person A sub 1, Person A sub 1 sub 1, Person A sub 1 sub 1 sub 1, Person A sub 1 sub 1 sub 1 sub 1, and Person A sub 1 sub 1 sub 1 sub 1 sub 1
Me: can't you just say Person A, Person B, Person C, Person D, Person E, and Person F?
Teacher: Shut up idiot & takes out stick
Me: Takes phone and is about to call my parents
Teacher: Ok let's go with your idea
😂
i still dont get what the word permutation means
Martin Bartsch hi
Martin Bartsch permutations= Total possible no. of ways to arrange a particular thing
I came for combinations not permutations
this is just intro video...
watch the next lessons from the "video dscription"...
10th like btw :O
Who else is here bc of corona?
Me
1:39 27?
3:20 You could have KFC
Well, you have actually not explained how to calculate combinations in the first place! You explained how to calculate permutations but how on earth should I know how to calculate combinations if I do not do permutations first?
these are episodic lessons, watch next video for combination formula
6!/(6-3)!3!
3:45 was a legendary aha moment for me!
what about 5 in 4?
permutation: 120
combination: 5
Anyone know who narrates this ?
The image is too offensive
❗❗❗❗❗❗❗❗❗
URGENT PLEASE🙏🏽
There are 12 numbers and 12 Alphabets.
And each number corresponds to an alphabet.
Its in the form below.
1 A
2 B
3 C
4 D
5. E
6. F
7 G
8 H
9 I
10 J
11 K
12 L
We are finding the combinations.
1. Find all the possible combination of these 24 entities in 12 groups. If number ( 1 ) occurs, it means alphabet ( A ) cannot occur . if ( 2 ) occurs, then alphabet ( B ) cannot occur. And so forth. How do you find such a combination ?
2. What are the list of all the combinations?
Is there any machine or app that can list all those combinations ? Lemme know
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est?
Because this book I have makes no sense
No thinking required to get the combinations:
A B C
A B D
A B E
A B F
A C D
A C E
A C F
A D E
A D F
A E F
B C D
B C E
B C F
B D E
B D F
B E F
C D E
C D F
C E F
D E F
So then I was thinking, what would be an organized, "no-thinking-required" way to get all the permutations?
1.) Keep the order of the combinations
2.) 2 other letters: Add one permutation with them, from left to right
3.) 2 other letters: Add one permutation with them, from right to left
. . . for each of the 20 combinations
. . . and this will get you 120
. . . as seen in the video:
ABC ACB BCA BAC CAB CBA
BCF BFC CFB CBF FBC FCB
It helps to do this in Excel vs. Handwriting it down!
very bad exolanation
It's explanation not exo lanation😂😂
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